Abstract

The use of diffractive beam-shaping elements in hybrid or monolithic microsystems is investigated. Compact optical systems require diffractive structures with small grating periods for creating large deflection angles. Such elements are difficult to fabricate while a low stray-light level is maintained. In addition, because of the small geometrical dimensions and the short propagation lengths in an optomechanical microsystem, any stray light generated by the diffractive structure critically affects the overall optical performance. A model for the estimation of the interference effects between the designed and the unwanted diffraction orders is developed and applied to an example of a collimating diffractive optical element. On the basis of theoretical and experimental results, design rules for the application of diffractive beam-shaping elements in microsystems are derived.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
    [CrossRef]
  2. Th. Hessler, M. Rossi, R. E. Kunz, M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
    [CrossRef]
  3. T. Fujita, H. Nishihara, J. Koyama, “Blazed gratings and Fresnel lenses fabricated by electron-beam lithography,” Opt. Lett. 7, 578–580 (1982).
    [CrossRef] [PubMed]
  4. M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
    [CrossRef]
  5. E. G. Loewen, S. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 11.
  6. R. E. Kunz, “Miniature integrated optical modules for chemical and biochemical sensing,” Sensors Actuators B 38–39, 13–28 (1997).
    [CrossRef]
  7. P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
    [CrossRef]
  8. See, for example, zemax, Version 7.0, produced by Focus Software, Inc., Tucson, Ariz. 85731;code v, Version 8.30, produced by Optical Research Associates, Pasadena, Calif. 91107; and solstis, Version 4.6, produced by Optis SA, 83078 Toulon, France.
  9. M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  10. D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 187–211.
  11. M. Ekberg, F. Nikolajeff, M. Larsson, S. Hård, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
    [CrossRef] [PubMed]
  12. M. Rossi, R. E. Kunz, H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. 34, 5996–6007 (1995).
    [CrossRef] [PubMed]
  13. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17, p. 64.
  14. D. A. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
    [CrossRef] [PubMed]
  15. T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
    [CrossRef]
  16. F. Nikolajeff, S. Hard, B. Curtis, “Diffractive microlenses replicated in fused silica for excimer laser-beam homogenizing,” Appl. Opt. 36, 8481–8489 (1997).
    [CrossRef]
  17. Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1997), Chap. 2.3.3.

1998 (1)

1997 (3)

F. Nikolajeff, S. Hard, B. Curtis, “Diffractive microlenses replicated in fused silica for excimer laser-beam homogenizing,” Appl. Opt. 36, 8481–8489 (1997).
[CrossRef]

R. E. Kunz, “Miniature integrated optical modules for chemical and biochemical sensing,” Sensors Actuators B 38–39, 13–28 (1997).
[CrossRef]

M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
[CrossRef]

1995 (1)

1994 (2)

M. Ekberg, F. Nikolajeff, M. Larsson, S. Hård, “Proximity-compensated blazed transmission grating manufacture with direct-writing, electron-beam lithography,” Appl. Opt. 33, 103–107 (1994).
[CrossRef] [PubMed]

M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

1992 (1)

1991 (1)

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

1982 (1)

1980 (1)

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

Akivis, M.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Buralli, D. A.

Curtis, B.

Ekberg, M.

Fujita, T.

Gale, M. T.

Th. Hessler, M. Rossi, R. E. Kunz, M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
[CrossRef]

M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Hard, S.

Hård, S.

Herzig, H. P.

Hessler, Th.

Th. Hessler, M. Rossi, R. E. Kunz, M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
[CrossRef]

Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1997), Chap. 2.3.3.

Holz, M.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Kedmi, J.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Knowlden, R. E.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Kobrin, B.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Kosoburd, T. P.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Koyama, J.

Kunz, R. E.

Larsson, M.

Loewen, E. G.

E. G. Loewen, S. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 11.

Malkin, Y.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Medeiros, S. S.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Morris, G. M.

Motamedi, M. E.

M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
[CrossRef]

Nikolajeff, F.

Nishihara, H.

Pedersen, J. S.

M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Pister, K. S. J.

M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
[CrossRef]

Popov, S.

E. G. Loewen, S. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 11.

Rhodes, P. W.

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

Ricks, D. W.

D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 187–211.

Rossi, M.

Schütz, H.

M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Shealy, D. L.

P. W. Rhodes, D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 20, 3545–3553 (1980).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17, p. 64.

Stern, M. B.

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Wu, M. C.

M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
[CrossRef]

Appl. Opt. (6)

J. Vac. Sci. Technol. B (1)

M. B. Stern, M. Holz, S. S. Medeiros, R. E. Knowlden, “Fabricating binary optics: process variables critical to optical efficiency,” J. Vac. Sci. Technol. B 9, 3117–3121 (1991).
[CrossRef]

Opt. Eng. (2)

M. E. Motamedi, M. C. Wu, K. S. J. Pister, “Micro-opto-electro-mechanical devices and on-chip optical processing,” Opt. Eng. 36, 1282–1297 (1997).
[CrossRef]

M. T. Gale, M. Rossi, J. S. Pedersen, H. Schütz, “Fabrica-tion of continuous-relief microoptical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Opt. Lett. (1)

Sensors Actuators B (1)

R. E. Kunz, “Miniature integrated optical modules for chemical and biochemical sensing,” Sensors Actuators B 38–39, 13–28 (1997).
[CrossRef]

Other (6)

D. W. Ricks, “Scattering from diffractive optics,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Vol. CR49 of SPIE Critical Reviews (SPIE, Bellingham, Wash., 1993), pp. 187–211.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 17, p. 64.

T. P. Kosoburd, M. Akivis, Y. Malkin, B. Kobrin, J. Kedmi, “Beam shaping with multilevel elements,” Diffractive and Holographic Optics Technology, I. Cindrich, S. H. Lee, eds., Proc. SPIE2152, 214–224 (1994).
[CrossRef]

Th. Hessler, “Continuous-relief diffractive optical elements: design, fabrication and applications,” Ph.D. dissertation (University of Neuchâtel, Neuchâtel, Switzerland, 1997), Chap. 2.3.3.

E. G. Loewen, S. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 11.

See, for example, zemax, Version 7.0, produced by Focus Software, Inc., Tucson, Ariz. 85731;code v, Version 8.30, produced by Optical Research Associates, Pasadena, Calif. 91107; and solstis, Version 4.6, produced by Optis SA, 83078 Toulon, France.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Two-element beam-shaping device for grating-pad illumination used in an optical microsystem and (b) the resultant irradiance.

Fig. 2
Fig. 2

Different types of DOE profile errors: (a) etch errors, (b) convolution with the writing beam, (c) a multilevel approximation.

Fig. 3
Fig. 3

Desired and unwanted diffraction orders in a collimating diffractive lens. Only the zeroth and the second diffraction orders are shown as examples for all the stray-light orders.

Fig. 4
Fig. 4

(a) Geometrical arrangement of the designed and the stray-light diffraction orders for a focusing diffraction lens. (b) Calculated irradiance distribution in the focal plane for a focusing diffractive lens with f = 1000 µm and illuminated by a Gaussian beam of λ = 1.0 µm and w 0 = 200 µm.

Fig. 5
Fig. 5

Normalized gray-scale representations of the irradiance at a distance of z = 2f behind the collimating lens for various diffraction efficiencies. The graphs show a one-dimensional sections through the centers of the irradiance distributions. Diffraction efficiencies: (a) η1 = 100%; (b) η1 = 99%, η0 = 0.3%, η-1 = 0.4%, and η-2 = 0.3%; (c) η1 = 96%, η0 = 1%, η-1 = 1%, η-2 = 0.5%, η-3 = 0.5%, and η2 = 1%; (d) η1 = 83%, η0 = 5%, η-1 = 4%, η-2 = 3%, η-3 = 2%, η-4 = 1%, η2 = 1%, and η3 = 1%. Uniformity errors: (a) Γ = 0%, (b) Γ = 8.8%, (c) Γ = 13.5%, (d) Γ = 22.8%.

Fig. 6
Fig. 6

Irradiance of Fig. 5(d) at distances of (a) z = 2f, (b) z = 4f, (c) z = 8f. The same irradiance distributions as shown in Fig. 5(d) were assumed.

Fig. 7
Fig. 7

Uniformity error as a function of the distance from the DOE. The same configuration as for Fig. 5(d) was assumed.

Fig. 8
Fig. 8

Interference pattern of diffractive beam collimators with f = 100 µm at a distance of z = 3f behind the DOE: (a) A DOE with M = 3, a uniformity error of Γ ≈ 17%, and irradiance distributions of η3 = 96%, η0,1,2,4 = 1%. (b) A DOE with M = 1, a uniformity error of Γ ≈ 10%, and irradiance distributions of η1 = 96%, η0,-1,-2,2 = 1%.

Fig. 9
Fig. 9

Uniformity error as a function of the phase offset for a collimating lens: The stray-light distributions of (a) Fig. 5(c) and (b) Fig. 5(d). The stray-light distributions of Figs. 5(a)5(d) were calculated for Δϕ = 0°.

Tables (1)

Tables Icon

Table 1 Typical Causes of Diffraction-Efficiency Reduction in DOE’s and the Corresponding Distribution of Stray Light

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

fp=fMMp.
Iinterfx, y=p bpupx, y2.
bp=ηp,
p ηp=1.
upx, y=2π1/2q0pq0p+zw0×exp-i 2πλz+x2+y22q0p+z+iϕp,
q0p=k-1f-i λπw02-1.
γ>η11-η1 NF2,
Γ= |Iinterfx, y-I1x, y|dxdy I1x, ydxdy,
A0=πw02z21z+1f2.
zfNF2-1.
ϕdiffx, y=ϕx, y+Δϕmod2π
ϕp=pΔϕ.

Metrics